Question 341707


If you want to find the equation of line with a given a slope of {{{1/2}}} which goes through the point ({{{4}}},{{{5}}}), you can simply use the point-slope formula to find the equation:



---Point-Slope Formula---
{{{y-y[1]=m(x-x[1])}}} where {{{m}}} is the slope, and *[Tex \Large \left(x_{1},y_{1}\right)] is the given point


So lets use the Point-Slope Formula to find the equation of the line


{{{y-5=(1/2)(x-4)}}} Plug in {{{m=1/2}}}, {{{x[1]=4}}}, and {{{y[1]=5}}} (these values are given)



{{{y-5=(1/2)x+(1/2)(-4)}}} Distribute {{{1/2}}}



{{{y-5=(1/2)x-2}}} Multiply {{{1/2}}} and {{{-4}}} to get {{{-2}}}



{{{y=(1/2)x-2+5}}} Add 5 to  both sides to isolate y



{{{y=(1/2)x+3}}} Combine like terms {{{-2}}} and {{{5}}} to get {{{3}}} 



So the equation of the line with a slope of {{{1/2}}} which goes through the point ({{{4}}},{{{5}}}) is:


{{{y=(1/2)x+3}}} which is now in {{{y=mx+b}}} form where the slope is {{{m=1/2}}} and the y-intercept is {{{b=3}}}



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Jim